To help you locate information on your Civil War participant, let's follow the process of conducting research on a sample Civil War participant:
Esther Hill Hawks (1833-1906), a doctor who graduated from the New England Female Medical College, cared for black troops serving in the Union Army.
Image from: amazon.com
Examples of resources in which to begin searching:
These types of resources can be great sources of concise background material on a topic, biographical information about individuals, etc.
FYI--Check out the reference lists at the end of encyclopedia articles. Some of those sources may be worth tracking down!
Examples of resources linked under the Primary Sources link in which to begin searching: